Thus, for each $1 ticket you purchase, you can expect to win 61 cents
back on the average. You can, however, expect to lose a net 39 cents on
each ticket.

Expected Winnings of a Lottery Ticket

The expected gross winnings of a lottery ticket is equal to
the average gross amount that a person will win for each ticket
purchased.

Example

If the expected gross winnings of a $1 lottery
ticket are $0.56, how much money will a person win expect to win by
purchasing 1000 lottery tickets?

Since the person wins $0.56 per ticket, the person could expect to
win 1000 x $0.56 = $560 by purchasing 1000 tickets. The expected net
winnings are not $560 however since the 1000 tickets cost $1000.

By factoring in the purchase price, the net expected loss is
$560 - $1000 = ($440).

Note that expected gross winnings do not indicate the actual amount
of money but the expected amount of money that a person will win.
The person could purchase the “big-winner” ticket and win much more than
$560. Also, the person could win less than $560. Expected gross winnings
merely indicates the “average” gross amount a person will win.

Lottery ticket “facts” are given here.

LOTTERY TICKET FACTS

The expected gross
winnings of a lottery ticket indicates the average amount of
winnings per ticket.

When a very large
number of lottery tickets are purchased, the average gross winnings
per ticket will be very close to the expected gross winnings
of the ticket.

If all of the
available tickets are purchased, the average gross winnings per
ticket are equal to the expected gross winnings.

In the long run,
a person experiences a net loss through the purchase of
lottery tickets.

In the short run,
a person “can sometimes beat the odds” and experience a net
gain through the purchase of lottery tickets.

Assignment 8

Go to
http://www.lottery.state.mn.us/wildhare.html. Use the lottery scratch game calculator shown
below to or use a scientific calculator to calculate the expected
gross winnings of a single one dollar ticket. Also, show the
calculations required in addition to the answer, even if you used the
scratch game calculator.

If you purchased 1000 of these tickets, what
would your net loss be?

If there were a game with expected gross
winnings of $0.74 for each dollar ticket sold and there were a total
of one million dollar tickets distributed, what would it cost to buy
all the tickets and how much would you win back?

Would it help your expected winnings if you
and 9 other people bought a total of 100 tickets in the wildhare game
above and split your earnings? Why or why not? In other
words, would you win more by pooling your resources with 9 others
rather than buying only 10 tickets yourself?

How does computing expected value of these
tickets help a person to maintain a sensible perspective on purchasing
lottery scratch game tickets?

This Scratch-type Game Expected Winnings Calculator calculates the
average amount you could expect to win per ticket. Fill in all the
entries. If you don't have 15 prizes, then place ZERO for Amount of
Prize and any NONZERO numbers for the odds for EACH non-prize. NO dollar
signs! Scroll down and click on CALCULATE. What
does all this mean?

Enter ZEROS for
non-prizes

Enter NON-Zero
values for non-prizes

Amount of Prize 1

Odds of winning prize
1 out of

Amount of Prize 2

Odds of winning prize
2 out of

Amount of Prize 3

Odds of winning prize
3 out of

Amount of Prize 4

Odds of winning prize
4 out of

Amount of Prize 5

Odds of winning prize
5 out of

Amount of Prize 6

Odds of winning prize
6 out of

Amount of Prize 7

Odds of winning prize
7 out of

Amount of Prize 8

Odds of winning prize
8 out of

Amount of Prize 9

Odds of winning prize
9 out of

Amount of Prize 10

Odds of winning prize
10 out of

Amount of Prize 11

Odds of winning prize
11 out of

Amount of Prize 12

Odds of winning prize
12 out of

Amount of Prize 13

Odds of winning prize
13 out of

Amount of Prize 14

Odds of winning prize
14 out of

Amount of Prize 15

Odds of winning prize
15 out of

Expected Winnings per Ticket

Calculated

Gambling Calculator Copyright 2003 Mike Sakowski - for
educational use only
Most, if not all, scratch-type games use "odds" to stand for
probabilities.
This calculator uses those "odds" as the probabilities input into the
expected value formula.

What does all
this mean? If you pay $1 for a ticket, and your expected winnings
are $0.72, then you would expect a net loss of $0.28 per ticket. Hence,
if you bought 100 tickets, you would experience a net loss of $28! The
more you buy, the more you lose!

SakowskiMath HOME All
material on this page can be provided in alternative formats upon request,
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